On using pairwise comparison in the analytic hierarchy process: Validity is goal while consistency is means

Abstract

To improve the quality of decision-making, the judgments of experts should be properly elicited. Pairwise Comparison (PC), kernel of the Analytic Hierarchy Process (AHP), is a prevalent method to manifest human judgments in Multiple Criteria Decision Making (MCDM). This study proposes a pragmatic guideline for using the PC matrix in the AHP to help decision makers (DMs) improve their decisions. First, extensive computer simulations indicate that, without strong evidence of linear relationship between an inconsistency index of a PC matrix and validity of priority vector derived from that matrix, it is questionable to set a threshold for this index to determine whether a PC matrix acceptable. Second, to resolve this problem, we propose a scale-validity (SV) index as an effective proxy for evaluating the validity of derived priority vector. Third, by integrating two paradigms (deterministic vs. statistical), we suggest a pragmatic guideline for DMs who have different epistemological views of inconsistency in order to improve their decision when using the AHP. To demonstrate the effectiveness and superiority of the proposed method, four examples of comparative analysis are illustrated. Finally, we summarize the results, contributions, and suggestions.